A control technique of multilevel converter topologies based on Direct Lyapunov Control method is presented in this paper for integration of Distributed Generation (DG) resources into the power grid. The compensation of instantaneous variations in the reference current components in ac-side and dc-voltage variations of cascaded capacitors in dc-side of the interfacing system are considered properly, which is the main contribution and novelty of this work in comparison with other control strategies. The proposed control technique provides the continuous injection of active power in fundamental frequency from DG sources to the grid. In addition, reactive power and harmonic current components of loads are provided with a fast dynamic response; thereby, achieving sinusoidal grid currents in phase with load voltages, while the required power from load side is more than the maximum capacity of interfaced converter, is possible. Simulation results confirm the effectiveness of the proposed control strategy in DG technology during dynamic and steady-state operating conditions.